System and methods for cross-sensor linearization

ABSTRACT

A method includes obtaining a plurality of master sensor responses with a master sensor in a set of training fluids and obtaining node sensor responses in the set of training fluids. A linear correlation between a compensated master data set and a node data set is then found for a set of training fluids and generating node sensor responses in a tool parameter space from the compensated master data set on a set of application fluids. A reverse transformation is obtained based on the node sensor responses in a complete set of calibration fluids. The reverse transformation converts each node sensor response from a tool parameter space to the synthetic parameter space, and uses transformed data as inputs of various fluid predictive models to obtain fluid characteristics. The method includes modifying operation parameters of a drilling or a well testing and sampling system according to the fluid characteristics.

BACKGROUND

Current practice in optical sensor calibration is typically performed ona sensor-by-sensor basis, applying a standard procedure to each opticalsensor and using the same number of reference fluids for all opticalsensors involved. Attempts to reduce the number of reference fluids in acalibration procedure may over-fit the selected data sets and fail toadequately generalize results for downhole application fluids. This isespecially problematic for calibration techniques adopting a non-linearmapping algorithm. On the other hand, increasing the number ofcalibration fluids for each optical sensor has the drawback of lowsafety and high cost.

Adding to the complexity of current strategies for standardizing opticalsensor response is the desire to perform reference measurements ofcalibration fluids at multiple temperature settings, multiple pressuresettings, and different combinations of temperature and pressuresettings. Combining measured and simulated optical sensor responses onreference fluids has been an attractive technique to solve thecalibration and standardization problem. However, cross-correlation ofoptical sensor data from multiple reference fluids may be non-linearwhen no spectral correction is available for each optical sensor. Whenthe cross-correlation is non-linear, it is difficult to develop a methodapplicable to additional reference fluids based on the measurements of areduced number of reference fluids. What is missing in optical sensorcalibration and standardization techniques is a cross-sensor datalinearization method applicable over different optical element designsand different optical sensor configurations in optical tool parameterspace.

BRIEF DESCRIPTION OF THE DRAWINGS

The following figures are included to illustrate certain aspects of thepresent disclosure, and should not be viewed as exclusive embodiments.The subject matter disclosed is capable of considerable modifications,alterations, combinations, and equivalents in form and function, withoutdeparting from the scope of this disclosure.

FIG. 1 illustrates a calibration system used to calibrate one or moreoptical elements.

FIG. 2 illustrates a general transformation model framework including aforward transformation and a reverse transformation with neuralnetworks.

FIG. 3 depicts a hierarchical structure for reverse transformationmodels.

FIG. 4 illustrates a schematic flowchart of a general method forcross-sensor linearization, and its application for improving reversetransformation and fluid characterization.

FIGS. 5A-5C illustrate a cross-sensor linearization procedure for asensor channel including an integrated computational element (ICE) formeasuring methane (‘methane ICE’).

FIGS. 6A-6C illustrate a cross-sensor linearization procedure for asensor channel including a Gas-Oil-Ratio (GOR) ICE.

FIGS. 7A-7C illustrate a cross-sensor linearization procedure for asensor channel including an Aromatics (ARO) ICE.

FIGS. 8A-8C illustrate a cross-sensor linearization procedure for asensor channel including a Saturates (SAT) ICE.

FIG. 9 illustrates a schematic flowchart of a method to be implementedfor cross-sensor linearization, and its application for improvingreverse transformation and fluid characterization.

FIG. 10 illustrates a schematic flowchart of a method for cross-sensorlinearization with use of a pre-processing procedure to prepare matcheddata pairs for master sensor and node sensor.

FIG. 11 illustrates a schematic flowchart of a method for cross-sensorlinearization with use of a two-dimensional temperature and pressureinterpolation scheme for correcting synthetic sensor response andgenerating optimized model coefficients on the training fluids.

FIG. 12 illustrates a schematic flowchart of a method for cross-sensorlinearization by estimating and including a node sensor response for anextended set of reference fluids for robust reverse transformation.

FIG. 13 is a drilling system configured to use a calibrated opticalsensor for modifying a drilling parameter or configuration in ameasurement-while-drilling (MWD) and a logging-while-drilling (LWD)operations.

FIG. 14 is a wireline system configured to use a calibrated opticalsensor during formation testing and sampling.

DETAILED DESCRIPTION

The present disclosure relates to calibration of optical sensors fordownhole optical fluid analysis and enhancement of optical sensortechnology. More specifically, the present disclosure provides a methodfor cross-sensor linearization to improve tool standardization.

Optical computing devices, also commonly referred to as“opticoanalytical devices,” can be used to analyze and monitor asubstance in real time. Such optical computing devices will often employan optical element or optical processing element that opticallyinteracts with the substance or a sample thereof to determinequantitative and/or qualitative values of one or more physical orchemical properties of the substance. The optical element may be, forexample, an integrated computational element (ICE), also known as amultivariate optical element (MOE), which is essentially an opticalinterference-based device that can be designed to operate over acontinuum of wavelengths in the electromagnetic spectrum from the UV tomid-infrared (MIR) ranges, or any sub-set of that region.Electromagnetic radiation that optically interacts with a substance ischanged and processed by the ICE so as to be readable by a detector,such that an output of the detector can be correlated to the physical orchemical property of the substance being analyzed. Other examples ofoptical elements may include band-pass filters, notch filters, neutraldensity filters, beam-splitters, polarizing beamsplitters, prisms,diffraction gratings, Fresnel lenses, and the like.

An ICE (hereafter “ICE core”) typically includes a plurality of opticallayers consisting of various materials whose index of refraction andsize (e.g., thickness) may vary between each layer. An ICE core designrefers to the number and thickness of the respective layers of the ICEcore. The layers may be strategically deposited and sized to selectivelypass predetermined fractions of electromagnetic radiation at differentwavelengths configured to substantially mimic a regression vectorcorresponding to a particular physical or chemical property of interestof a substance. Accordingly, an ICE core design will exhibit atransmission function that is weighted with respect to wavelength. As aresult, the output light intensity from the ICE core conveyed to adetector may be related to the physical or chemical property of interestfor the substance.

The terms “optical computing device” and “optical sensor” are usedherein interchangeably and refer generally to a sensor configured toreceive an input of electromagnetic radiation that has interacted with asubstance and produced an output of electromagnetic radiation from anoptical element arranged within or otherwise forming part of the opticalcomputing device. The processing element may be, for example, an ICEcore as described above. Prior to field use, the optical computingdevice, and each optical element employed therein, is calibrated suchthat each is able to operate effectively upon being exposed to downholeconditions. When an optical computing device is not properly calibrated,the resulting transmission functions derived from each optical elementmay provide well operators with inaccurate measurements upon deployment.

After manufacture, and before being placed in downhole use, each opticalcomputing device is carefully calibrated against known reference fluidsfor temperature and pressure ranges expected to be encountered in thefield. The calibrated optical computing devices are then installed aspart of a downhole tool and re-tested to validate the optical responsesfrom the optical element.

Embodiments described herein provide methods and systems for calibratingand standardizing optical sensor response during tool validation testingand field testing. Moreover, the presently described methods improvetool standardization by using a cross-sensor linearization of opticalchannel responses associated with a plurality of optical sensors. Moreparticularly, a method is provided for optical sensor standardization,which may be applicable to pressure-volume-temperature (PVT)characterization of a downhole fluid, for optical sensor manufacturingcalibration, for tool validation testing, and for field datapost-processing.

Downhole optical fluid processing often starts with data mapping toconvert optical sensor measurements into compatible inputs of variouspre-determined fluid characterization models. A fluid characterizationmodel may include fluid composition models to determine the differentcomponents of a fluid, such as a Gas-Oil-Ratio (GOR), an aromaticscontent, or a saturated hydrocarbon content. In some embodiments, fluidcomposition models include property predictive models of the fluid, suchas viscosity, density, or phase (solid, liquid, gas, or a combination).A data mapping algorithm, also called ‘reverse transformation’ or‘instrument standardization’ algorithm, is built on a set of referencefluids through manufacturing calibration. To ruggedize downhole fluidanalysis, quality data transformation through a reasonable selection ofreference fluids is desirable to develop a reliable reversetransformation. Candidate reference fluids in general are chosen fromgood representatives of formation/petroleum fluids. Furthermore,reference fluids are measured over a wide range of temperature andpressure settings to better simulate downhole conditions whilemaintaining safe laboratory operating conditions. It is desirable toobtain a wide dynamic range in optical sensor responses during thecalibration measurements. Embodiments disclosed herein allow a suitabletrade-off between using adequate number of reference fluids for robustcalibration and minimizing total operational cost, according to thespecific measurement conditions.

Embodiments consistent with the present disclosure include linearizing across-correlation of data from multiple sensors and for multiplereference fluids. In some embodiments, the data is obtained with opticalsensors selected within the same fabrication/calibration batch. In someembodiments, the data is obtained from optical sensors selected amongdifferent fabrication batches and with the same design. In otherembodiments, the data may be obtained from optical sensors selectedamong different designs having the same optical sensor configuration. Inyet other embodiments, the data is obtained from optical sensorsselected from different designs, having different sensor configurations.

In some embodiments, calibration against a full-set of reference fluidsis performed on a selected number of ‘master sensors’ duringmanufacturing. Other sensors in the manufacturing batch, or in adifferent batch, are calibrated against a reduced-set of referencefluids. These sensors are referred to as ‘node sensors.’ The reduced-setof reference fluids may be a plurality of reference fluids that are safeand cost-effective to operate in laboratory conditions. A reversetransformation algorithm is built using data collected from the full-setof reference fluids. To obtain the reverse transformation, master sensordata may include only measured optical responses on the full-set ofreference fluids. On the other hand, node sensor data may include ahybrid set having measured optical responses from the reduced-set ofreference fluids, and simulated optical responses from reference fluidsin the full-set of reference fluids that are not included in thereduced-set of reference fluids. In that regard, some embodiments use alinear or near-linear transformation algorithm using compensated mastersensor responses as input for simulating the optical responses for nodesensors against the reference fluids in the full-set of referencefluids. The transformation algorithm is based on a channel-by-channeldata correlation on the reduced-set of reference fluids between themaster sensor and the node sensor. The specific type of optical elementused in optical sensors according to embodiments disclosed herein mayinclude ICE cores or other types of optical devices or elements, such asnarrow band-pass (NBP) filters and the like. In general, embodimentsdisclosed herein are consistent with any type of optical device orelement used in an optical sensor. Embodiments of the present disclosureare particularly desirable when a non-linear correlation between amaster sensor response and a node sensor response is observed for areduced-set of reference fluids.

In some embodiments, a method includes obtaining a plurality of mastersensor responses with a master sensor in a set of training fluids andobtaining node sensor responses in the set of training fluids. Themethod further includes finding a linear correlation between acompensated master data set and a node data set for a set of trainingfluids and generating node sensor responses in a tool parameter spacefrom the compensated master data set on a set of application fluids.Further, the method includes obtaining a reverse transformation based onthe node sensor responses in a complete set of calibration fluids, thereverse transformation transforming each node sensor response from atool parameter space to the synthetic parameter space and obtainingfluid characteristics using reverse-transformed inputs. The methodincludes modifying operation parameters of a drilling or a well testingand sampling according to the fluid characteristics.

In some embodiments, a method includes determining an estimated valuefor a node sensor response in synthetic parameter space using atwo-dimensional interpolation for temperature and pressure, anddetermining an estimated value for a master sensor response in syntheticparameter space using the two dimensional interpolation for temperatureand pressure. The method further includes determining a differencebetween the estimated value for a node sensor response and the estimatedvalue for a master sensor response, determining a set of cross-sensorlinearized model coefficients in an optimization loop, and adjusting amaster sensor channel selection to simulate a particular channelresponse of the node sensor. Further, the method includes storing a setof cross-sensor linearized model coefficients for a node sensor channel,and modifying operation parameters of a drilling or a well testing andsampling according to a fluid characteristic obtained with a reversetransformation and a synthetic fluid predictive model. The reversetransformation is obtained using the stored set of cross-sensorlinearized model coefficients.

In yet other embodiments, a method, includes introducing a tool into awellbore drilled into one or more subterranean formations, the toolhaving been previously calibrated for operation by performing a numberof steps. The steps for calibrating the tool may include: obtaining aplurality of master sensor responses with a master sensor in a set oftraining fluids, obtaining a plurality of node sensor responses with aplurality of node sensors in the set of training fluids, each of theplurality of node sensors and the master sensor including an opticalelement, finding a linear correlation between a compensated master dataset and a node data set for a set of training fluids, generating aplurality of node sensor responses in a tool parameter space from thecompensated master data set on a set of application fluids, andobtaining a reverse transformation based on the plurality of node sensorresponses in a complete set of calibration fluids, wherein the completeset of calibration fluids comprises the set of training fluids and theset of application fluids. The method further includes determining afluid characteristic from the plurality of node sensor responses in thesynthetic parameter space using the reverse transformation and asynthetic fluid predictive model, and modifying operation parameters ofa drilling or a well testing and sampling according to the fluidcharacteristic.

FIG. 1 illustrates an exemplary manufacturing calibration system 100that may be used to calibrate one or more optical elements used in anoptical sensor. As illustrated, system 100 may include a measurementsystem 102 in optical communication with one or more optical elements104 (shown as 104 a, 104 b, 104 c . . . 104 n) that are to becalibrated. Each optical element 104 a-n may be either an opticalband-pass filter or a multivariate optical element/integratedcomputational element (e.g., an ICE core). The measurement system 102may circulate one or more reference fluids with different chemicalcompositions and properties (i.e., methane concentration, aromaticsconcentration, saturates concentration, GOR, etc.) through an optic cell106 over widely varying calibration conditions of temperature, pressure,and density, such that optical transmission and/or reflectionmeasurements of each reference fluid in conjunction with each opticalelement 104 a-n may be made at such conditions.

The measurement system 102 may comprise an opticalpressure-volume-temperature (PVT) instrument, and the reference fluidscirculated in the measurement system 102 may comprise representativefluids commonly encountered in downhole applications. System 100 maycollect output signals from each optical element 104 a-n for eachspecified reference fluid at varying calibration conditions. In somecases, the reference fluids may comprise seven representative fluidsthat are easy to operate for manufacturing calibration, namely,dodecane, nitrogen, water, toluene, 1-5 pentanediol, and two liquidcrude oils or fluids with no gas concentration (e.g., dead oil). Thecrude reservoir oils used as reference fluids may be, for example,global oil library 13 (or “GOL13”), and global oil library 33 (or“GOL33”). In other cases, the reference fluids may include samples oflive oils mixed with dead oil and hydrocarbon gas, such as methane forexample, and the samples of hydrocarbon gases and/or CO₂. Manufacturingcalibration of the optical sensor may serve the need of detector outputre-scaling or instrument standardization.

The measurement system 102 may vary each reference fluid over severalset points spanning varying calibration conditions. To accomplish this,as illustrated, the measurement system 102 may include a liquid chargingsystem 108, a gas charging system 110, a temperature control system 112,and a pressure control system 114. The liquid charging system 108injects reference fluids into the fluid circuit to introduce fluidvarying perturbations such that calibrating the optical elements 104 a-nwill incorporate all the expected compounds found in the particularreference fluid. The gas charging system 110 may inject known gases(e.g., N₂, CO₂, H₂S, methane, propane, ethane, butane, combinationsthereof, and the like) into the circulating reference fluids. Thetemperature control system 112 may vary the temperature of the referencefluid to simulate several temperature set points that the opticalelements 104 a-n may encounter downhole. Lastly, the pressure controlsystem 114 may vary the pressure of the reference fluid to simulateseveral pressure set points that the optical elements 104 a-n mayencounter downhole.

The optic cell 106 is fluidly coupled to each system 108, 110, 112, and114 to allow the reference fluids to flow therethrough and recirculateback to each of the systems 108, 110, 112, and 114 in a continuous,closed-loop fluid circuit. While circulating through the optic cell 106,a light source 116 emits electromagnetic radiation 118 that passesthrough the optic cell 106 and the reference fluid flowing therethrough.As the electromagnetic radiation 118 passes through the optic cell 106it optically interacts with the reference fluid and generates sampleinteracted light 120, which includes spectral data for the particularreference fluid circulating through the measurement system 102 at thegiven calibration conditions or set points. The sample interacted light120 may be directed toward optical elements 104 a-n which, asillustrated, may be arranged or otherwise disposed on a sensor wheel 122configured to rotate in the direction A. While shown as arranged in asingle ring on the sensor wheel 122, optical elements 104 a-n mayalternatively be arranged in two or more rings on the sensor wheel 122.

During calibration, the sensor wheel 122 may be rotated at apredetermined frequency such that each optical element 104 a-n mayoptically interact with the sample interacted light 120 for a briefperiod and sequentially produce optically interacted light 124 that isconveyed to a detector 126. The detector 126 may be generallycharacterized as an optical transducer and may comprise, but is notlimited to, a thermal detector (e.g., a thermopile), a photoacousticdetector, a semiconductor detector, a piezo-electric detector, a chargecoupled device (CCD) detector, a video or array detector, a splitdetector, a photon detector (e.g., a photomultiplier tube), photodiodes,and any combination thereof. Upon receiving individually-detected beamsof optically interacted light 124 from each optical element 104 a-n, thedetector 126 may generate or otherwise convey corresponding responsesignals 128 to a data acquisition system 130. The data acquisitionsystem 130 may time multiplex each response signal 128 received from thedetector 126 corresponding to each optical element 104 a-n. Acorresponding set of resulting output signals 132 is subsequentlygenerated and conveyed to a data analysis system 134 for processing andproviding input parameters for various fluid predictive models with useof outputs from each optical element 104 a-n as a candidate variable.Data analysis system 134 may be coupled to a computer 140, which mayinclude a memory 142 and a processor 144. Memory 142 may store commandswhich, when executed by processor 144, cause computer 140 to perform atleast some of the steps in the methods described herein and otherwiseconsistent with the present disclosure.

Once the sensor wheel 122 is calibrated, one or more calibrated sensorwheels 122 may then be installed on an optical tool with other systemcomponents and otherwise placed in an optical computing device forassembly validation testing. To validate the optical response of thetool assembly, the optical tool may be placed in an oven that regulatesthe ambient temperature and pressure. The reference fluids used tocalibrate the sensor wheel 122 may then be selectively circulatedthrough the optical tool at similar set points used to calibrate theoptical elements 104 a-n. More particularly, the reference fluids may becirculated through the optical tool at various set point downholeconditions (i.e., elevated pressures and temperatures) to obtainmeasured optical responses.

While manufacturing calibration of the sensor wheel 104 a-n usingreference fluids is performed in a tool parameter space, fluidspectroscopic analysis and fluid predictive model calibration using alarge amount of data in a standard oil library is performed in asynthetic parameter space (also called Optical-PVT data space).Synthetic sensor responses of each element are calculated as a dotproduct of full-wavelength-range of fluid spectrometry and sensorelement spectrum excited by a light source, which might nonlinearly orlinearly vary in scale compared to the actual sensor response due to thedifference between the mathematic approximation used in calculatingsynthetic sensor response and the real system implementation. Tocompensate for the difference above, the measurement data from theoptical tool can be transformed from the tool parameter space to thesynthetic parameter space first through a reverse transformationalgorithm before applying fluid predictive models. Also, fluidpredictive models can be calibrated with different synthetic opticalinputs and saved in an optical fluid model base to provide sufficiencyand adaptation in dealing with uncertainty of data transformation andimproving formation fluid compositional analysis and field datainterpretation.

In current practice, an optical fluid model is sensor dependent,including data transformation (i.e., standardization) models andproperty predictive models. To provide adequate flexibility for opticaldata processing and interpretation, an optical fluid model includes thefollowing candidate constituents: transformation models calibrated onselected reference fluids through reverse transformation, transformationmodels calibrated on selected reference fluids through forwardtransformation, and predictive models calibrated on both Optical-PVTdatabase and sensor wheel 122 data spaces.

Transformation model development using selected reference fluidsrequires matched calibration data pairs of optical sensor responsessimulated in the synthetic parameter space and measured in a tool dataspace of sensor wheel 122. In synthetic parameter space, simulatedsensor responses on reference fluids are available at the idealtemperature and pressure setting points. Measured optical responses ofthe sensor wheel 122 may endure slight temperature and pressurevariation during manufacturing calibration. In some embodiments, matchedtransformation data pairs are obtained through two-dimensionalinterpolation by using actual temperatures and pressures as inputs togenerate simulated sensor responses at the corresponding measurementconditions. Depending on the data space in which the fluid propertypredictive models are calibrated, data transformation models convertmeasured or simulated optical sensor output between a tool data spaceand a synthetic parameter space. FIG. 2 illustrates one suchtransformation.

More particularly, FIG. 2 illustrates an embodiment of a generaltransformation model framework with a multi-input, multi-output neuralnetwork that may be applied by the data analysis system 134 of FIG. 1 tooptical responses. The model that converts the actual optical sensorresponse channels (SW/Ch01-Ch0 n) from tool parameter space 201 tosynthetic parameter space 202 (PVT/Ch01-Ch0 n) is a reversetransformation 203. The model that converts data from syntheticparameter space 202 into tool parameter space 201 is a forwardtransformation 205. Although the illustrated general transformationmodel framework in FIG. 2 is configured with multi-input/multi-outputnon-linear neural networks, there is no limitation in using othernon-linear and linear transformation algorithms withsingle-input/single-output and multi-input/single-output configurations.

FIG. 3 illustrates an embodiment of a hierarchical structure for reversetransformation models 302. The variations of transformation models 302may include converting optical channels 304 for each optical sensor in asingle model, converting the disjoined optical channels in severaldetector-based models 306, or converting only selected channels 308 ofinterest each time in different individual models. Compared to a singlemodel implementation, multi-model options can improve the reliability ofdata construction in the output (i.e., transformed) parameter domain(e.g., synthetic parameter space 202, cf. FIG. 2) if one or more of theoptical channels (e.g., tool parameter space 201, cf. FIG. 2), as atransformation input, experience a problem. A plurality of referencefluid blocks 310-320, at the bottom of the hierarchical structure andcoupled to the various channels 304-308, represent the transformationmodels that can be built based on different reference fluids (e g.,minimum number of reference fluids 310, 314, 318 and extended referencefluids 312, 316, 320). The minimum number of reference fluids may referto the seven representative fluids discussed above. These referencefluids are safe to use in a laboratory configuration and easy to cleanfor testing purposes. Optical sensor responses (e.g., tool parameterspace 201) generally have a wide dynamic range as a representation ofdiverse fluids in an existing Optical-PVT database. Extended referencefluids often include one or more fluids such as live oil and/or gas tocover a wider dynamic range and provide a more robust transformationmodel.

In some embodiments, reverse transformation 203 converts toolmeasurements from tool parameter space 201 into synthetic parameterspace 202 prior to applying fluid characterization models. Accordingly,fluid characterization models use data from synthetic parameter space202 as input to obtain information such as fluid composition, andphysical properties of the fluid. A forward transformation 205 can beused to convert a whole set of simulated optical sensor responses fromsynthetic parameter space 202 to tool parameter space 201 prior todeveloping predictive models on tool parameter space 201. As seen inFIG. 2, forward transformation 205 can be created by switching the inputand the output of a neural network model. In other words, using asynthetic-channel response as an input, and a measured sensor wheelchannel response as an output a neural network can then be trained tocalibrate forward transformation algorithms.

As will be appreciated, a hierarchical structure for the reversetransformation models 302, as illustrated in FIG. 3, can also be appliedto forward transformation models. After forward transformation 205 isdeveloped, it can be used to convert the synthetic sensor responses ofthe global samples in synthetic parameter space 202 into tool parameterspace 201. Then the fluid property predictive models can be calibratedin tool parameter space 201, and the further transformation is notneeded in field data processing because measured optical responses fromthe tool can be used as model inputs directly for fluid compositionalanalysis. Compared to the reverse transformation, which applies on-linetool data conversion each time before making a fluid prediction, forwardtransformation usually only applies one time off-line to convertsynthetic sensor responses for fluid prediction model development.

By applying a transformation model to the optical responses derived fromthe optical sensor, the optical sensor is calibrated for use and readyfor validation testing in any number of downhole tools. Such a sensor,calibrated over a full set of reference fluids, may be characterized andotherwise referred to herein as a ‘master sensor’. During toolvalidation testing, one or more master sensors may be installed in atool that is to be introduced downhole to obtain wellbore measurements.In some embodiments, as described below, the downhole tool may form partof a bottom hole assembly used in a drilling operation. In suchembodiments, the tool may comprise any of a number of different types oftools including MWD (measurement-while-drilling) tools, LWD(logging-while-drilling) tools, and others. In other embodiments,however, the tool may be used in a wireline operation and otherwise formpart of a wireline logging tool, such as a probe or sonde, to be loweredby wireline or logging cable into a borehole to obtain measurements.

In some embodiments, an optical sensor installed in a tool may becharacterized as a ‘node sensor,’ and at least some reference fluidsthat were used to calibrate the master sensor may be run through thenode sensor at the same or similar set points (i.e., elevated pressuresand temperatures). In some embodiments, the tool validation testing isundertaken at a laboratory facility. In such cases, the same referencefluids used to calibrate the optical sensor may be used. In other cases,however, or in addition to laboratory testing, tool validation testingmay be undertaken on-site, such as at a drill rig or wellheadinstallation where the tool is to be used in a wellbore operation. Insuch cases, a limited number of reference fluids may be used, such aswater and nitrogen. Optical responses derived from the tool duringvalidation testing may be normalized by using the transformation model(e.g., reverse transformation 203, forward transformation 205) to adjustthe output of the tool validation process. The optical responses maythen be compared against the optical responses of the master sensor.

FIG. 4 illustrates a flowchart including steps in a general method 400for cross-sensor linearization and its application for improving reversetransformation and fluid characterization, according to someembodiments. Method 400 may be performed by a computer device having amemory and a processor (e.g., computer 140, memory 142, and processor144, cf. FIG. 1). The memory may store commands that, when executed bythe processor, cause the computer to perform at least some of the stepsin method 400. Methods consistent with method 400 may include at leastone but not all of the steps in method 400, performed in any order.Furthermore, methods consistent with the scope of method 400 may includeat least some of the steps in method 400 performed overlapping in time,or even simultaneously. Methods consistent with method 400 may includemeasuring reference fluids with a measurement system using an opticalsensor having a plurality of optical elements (e.g., measurement system102 and optical elements 104 a-n, cf. FIG. 1). In some embodiments, theplurality of optical elements in method 400 may correspond to the sameoptical sensor, or may belong to different optical sensors. Accordingly,the plurality of optical elements in method 400 may be selected withinthe same fabrication batch, among the different fabrication batches,within the same optical element design, among different optical elementdesigns, within the same sensor configuration or among different sensorconfigurations. In some embodiments, the measurement system in method400 may include a reverse transformation or a forward transformationbetween sensor responses in tool parameter space and sensor responses insynthetic parameter space (e.g., tool parameter space 201, syntheticparameter space 202, reverse transformation 203, and forwardtransformation 205).

Step 402 includes obtaining a plurality of master sensor responses,P_(m), with a master sensor on a set of training fluids. In someembodiments, the set of training fluids is master set of referencefluids including a representative or comprehensive set of referencefluids for a downhole oil and gas exploration measurement. Step 404includes obtaining a plurality of node sensor responses, P_(n), with aplurality of node sensors on the set of training fluids. In someembodiments, the set of training fluids is a reduced set of referencefluids such as a sub-set of the master set of reference fluids.Accordingly, in some embodiments the master sensor and the node sensorseach measure the reduced set of reference fluids.

Step 406 includes selecting a weighting factor, C, to calculate aplurality of compensated master sensor responses with the plurality ofnode sensor responses. In some embodiments, step 406 includes master andnode sensor responses for the reduced set of reference fluids, which iscommon to both master and node sensors. Accordingly, step 406 includesobtaining compensated master sensor responses by adding the actualmeasured master sensor responses to the reduced set of reference fluidsto a weighted difference between a node sensor response in syntheticparameter space and a master sensor response in synthetic parameterspace. Sensor responses in synthetic parameter space are the Optical-PVTresponses used for fluid product calibration (cf. synthetic parameterspace 202, FIG. 2). In some embodiments, step 406 may includedetermining the spectral response of at least one optical element (e.g.,an ICE) in the optical sensor at either elevated temperature andpressure, or room temperature and pressure.

The weighted difference between responses from the master sensor and thenode sensors in synthetic parameter space incorporates cross-sensorvariations in optical signal intensity induced by a variation of theoptical elements. The variation between optical elements may be a resultof manufacturing fluctuations within the same fabrication batch. In someembodiments, the variation between optical elements may be a result ofvariations between different designs of the optical elements. In yetother embodiments, the variations between optical elements may be aresult of different optical sensor configuration. In some embodiments,step 406 includes selecting a weighting factor, C, in a mathematicalequation as shown below:

P _(cm) =P _(m) +C·(S _(n) −S _(m))  (1)

where P_(cm) is the compensated master sensor response on the reducedset of reference fluids in tool parameter space; and S_(n) and S_(m) arethe node sensor and master sensor responses, respectively, in thesynthetic parameter space on the same reduced set of reference fluids.The sensor response in synthetic parameter space at each channel is adot product (scalar product) of a fluid spectroscopic response vector(R_(fl)) and a convolved spectroscopic response vector of a particularoptical element (R_(oe)). In some embodiments, R_(fl) and R_(oe) arevectors in a wavelength parameter space. In that regard, the convolvedspectroscopic response may include a spectral emissivity of light source116 (FIG. 1), a band pass filter transmittance, or any otherspectroscopic response of the optical element. Accordingly, in someembodiments step 406 includes performing mathematical operations in thefollowing equation to find the synthetic node sensor and master sensorresponse (S_(n,m)):

S _(n,m) =R _(fl) ·R _(n,m)  (2)

Since the fluid spectroscopy (R_(fl)) is the same for S_(n) and forS_(m), the difference of (S_(n)−S_(m)) indicates the variation ofconvolved transmittance spectrum of node and master sensor elements(R_(n,m)). The weighting factor C in Eq. (1) is channel dependent. Insome embodiments, step 406 includes selecting a weighting factor C inEq. (1) from a validated range (between −3 to +3 with an increment stepof 0.1 for example) to optimize a linear correlation between thecompensated master sensor responses obtained from Eq.(1) and the nodesensor responses associated with the reduced set of reference fluids.Using the selected weighting factor C for each optical channel, a linearmodel correlating master sensor responses with node sensor responses forthe reduced set of reference fluids is obtained in step 408.

Step 408 includes finding a linear correlation between the compensatedmaster data set and the node data set for a set of training fluids. Moreparticularly, step 408 includes determining a linear correlation betweenthe compensated master sensor responses and a plurality of measured nodesensor responses, as follows:

P _(n) =k·P _(cm) +b  (3)

In some embodiments, the linear correlation expressed in Eq. (3)involves node sensor responses P_(n) in tool parameter space. In someembodiments, step 408 includes testing the linear correlation in Eq. 3with a selected value of C, according to step 406. When a new value of Cin step 406 renders a better linearization according to step 408, thenew value of C is preferred over the old value. When a selected value ofC optimizes the linear Eq. (3) on the reduced reference fluids, nodesensor responses on additional reference fluids would be robust againstdifferent variations of the optical elements. In some embodiments, step408 includes constructing synthetic node sensor responses over themaster set of reference fluids, using Eq. (2). The synthetic responseset may be denoted as:

S _(nf) =[S _(n) S _(nr)]

where S_(nf) is the full set of synthetic node sensor responses, S_(n)includes the synthetic node sensor responses corresponding to thereduced set of reference fluids, and S_(nr) includes the node sensorresponses in synthetic parameter space corresponding to the referencefluids in the master set that are not included in the reduced set. Insome embodiments, obtaining the response set S_(nr) in syntheticparameter space as illustrated above may include performing mathematicaloperations including vectors R_(fl) and R_(n) (cf. Eq. 2), which areknown from laboratory measurements or which may be retrieved fromlibrary databases.

Step 410 includes generating a plurality of node sensor responses in atool parameter space from the compensated master data set on a set ofapplication fluids. Step 410 includes calculating node sensor responseson additional fluids to complete the master set of reference fluids.After parameters C, k and b are determined on the reduced referencefluids (training fluids), embodiments consistent with the presentdisclosure simulate node sensor responses on additional reference fluids(application fluids) using the parameters C, k, and b (cf. Eqs. (1) and(3)). Step 410 includes obtaining a hybrid set of node sensor responsesin the tool parameter space for the master set of reference fluids. Thehybrid set may be denoted as:

P _(nf) =[P _(n) P _(nr)]

where P_(n) are the node sensor responses in tool parameter space forreference fluids in the reduced set, and P_(nr) are estimated nodesensor responses for reference fluids in the master set that are notincluded in the reduced set. To obtain the set P_(nr), in someembodiments, step 410 may include using the set S_(nr) and S_(mr)obtained in step 408 to determine a set of compensated master responsesaccording to Eq. (1), where the value of C is already selected. Once thecompensated master sensor responses are known, step 410 may includeusing the linear coefficients (k and b, cf. Eq. 3) found in step 408, toobtain the node sensor responses in tool parameter space for the fullset of reference fluids.

This application is especially useful for non-linear neural networkbased reverse transformation, in which multi-input and multi-outputmapping can be better implemented with wider range of data to robustlyconvert tool measurement data to the synthetic parameter space priorapplying fluid composition and property predictive models.

Step 412 includes obtaining a reverse transformation based on theplurality of node sensor responses on a complete set of calibrationfluids. According to some embodiments, the complete set of calibrationfluids comprises the set of training fluids and the set of applicationfluids. Step 412 includes obtaining a reverse transformation, f, betweena plurality of node sensor responses in tool parameter space P_(nf) anda plurality node sensor responses S_(nf) in synthetic parameter space.After simulated optical responses on additional reference fluids fornode sensors are calculated, the reverse transformation algorithmconverting optical responses from tool parameter space to syntheticparameter space for the full-set of reference fluids can be built. Step412 may include performing non-linear (as shown in FIG. 2) or linearregression analysis. Accordingly, a calibrated node sensor response maybe obtained using the reverse transformation, f, as follows:

S _(nf) =f(P _(nf))  (4)

Step 414 includes obtaining fluid characteristics with synthetic fluidpredictive models using reverse-transformed inputs from at least one ofthe node sensor responses to a fluid measurement. In some embodiments,step 414 includes implementing improved reverse transformationalgorithms and existing fluid characterization models on real-time dataprocessing software for downhole optical fluid analysis. When opticaldata associated with formation fluids is collected with downhole opticaltool, it is input to reverse transformation algorithm (e.g., functionfin Eq. (4)), then applied to pre-calibrated various fluid predictivemodels in determining fluid characteristics from the plurality oftransformed optical responses. Fluid predictive models are typicallycalibrated with synthetic optical sensor responses on large number offluid samples and diverse analyte data. In some embodiments, step 414may include at least one of developing, modifying, or using a fluidcharacterization algorithm in tool parameter space when actual opticalresponses of adequate number of petroleum fluids is collected on atypical master sensor or multiple sensors. Simulated node sensorresponses would include more petroleum fluids by using a cross-sensordata correlation analysis as described in steps 402-414. Moreover, step414 may include calibrating fluid composition and property predictivemodels using data in the tool parameter space directly with no need ofreverse transformation during field data processing. Accordingly, insome embodiments the reverse transformation ‘f’ of Eq. (4) may be usedto convert validated field data from the tool parameter space tosynthetic parameter space. The transformed field data may then becombined with existing lab data in synthetic parameter space, anddirectly incorporated into the development of fluid characterizationmodels, including fluid composition and property predictive models.

Step 416 includes modifying operation parameters for drilling or welltesting and sampling system according to the estimated fluidcharacteristics. A drilling parameter may be a drilling speed, adrilling configuration, such as steering the drill bit between avertical or quasi-vertical drilling configuration and a horizontal orquasi-horizontal drilling configuration. Further according to someembodiments, step 416 may include adjusting the port, rate and directionof pump-out during well testing after the drilling is completed toimprove the fluid sampling and contamination analysis.

A downhole optical tool according to embodiments disclosed herein isused with formation testing and sampling after drilling is complete.Accordingly, in some embodiments step 418 includes processing opticalsensor measurements with optional data correction and standardizationalgorithms to minimize the uncertainty of reverse transformation, andobtaining a robust estimation of the fluid characteristics to helpdecision-making.

FIGS. 5A-5C, FIGS. 6A-6C, FIGS. 7A-7C, and FIGS. 8A-8C demonstrate theapplications of the disclosed methods in four different scenarios,respectively. There are three subplots in each set of figures. The firstsubplot (FIGS. 5A, 6A, 7A, and 8A) compares the difference of theconvolved transmittance spectrum of ICE element between the master andnode sensor. The second subplot (FIGS. 5B, 6B, 7B, and 8B) shows themaster-node data correlation without spectra correction. The thirdsubplot (FIGS. 5C, 6C, 7C, and 8C) shows the linearized master-node datacorrelation using the invented method.

FIGS. 5A-5C illustrate a cross-sensor linearization procedure for asensor channel including a methane ICE, according to some embodiments.More particularly, FIGS. 5A-5C illustrate a scenario in which the mastersensor and node sensor are selected from the same batch of manufacturingcalibration with little temperature and pressure variation for each datapair. The sensor configurations are the same, and the optical elementdesign is also the same. Without limitation, the optical element inFIGS. 5A-5C is a methane ICE on the master and node sensors.

FIG. 5A illustrates chart 500A with a master sensor spectral response502 and a node sensor spectral response 504. Chart 500A includeswavelength in the abscissae and transmission in the ordinates. Spectralresponses 502 and 504 may be used in R_(n,m) for the calculation of thesensor response in synthetic parameter space (cf. Eq. (2) above).

FIG. 5B illustrates chart 500B with a data cross-correlation between themaster sensor and the node sensor illustrated in FIG. 5A. Accordingly,the abscissae 551 in chart 500B correspond to the master sensorresponses in tool parameter space. The ordinates 552 in chart 500Bcorrespond to the node sensor responses in tool parameter space. Themultiple data points in chart 500B correspond to a reduced set ofreference fluids, and are clustered as follows: data clusters 501 a-ccorrespond to GOL33; data clusters 503 a-c correspond to GOL13; dataclusters 505 a-c correspond to H₂O (water); data clusters 507 a-ccorrespond to toluene; data clusters 509 a-c correspond to 1-5pentanediol (PEN); data clusters 511 a-c correspond to dodecane (DOD);and data clusters 513 a-c correspond to N₂ (nitrogen). For each set a-cof data clusters, a different combination of temperature and pressuresettings was used to measure the specific reference fluid. The typicaltemperature and pressure setting points may include combinations ofthree temperatures (150, 200, 250 Fahrenheit) and four pressures (3000,6000, 9000 and 12000 PSI). Furthermore, within each data cluster, theindividual data points correspond to different data collection eventsfor the given reference fluid at the given temperature and pressuresetting.

The similarity between master sensor and node sensors in the specificcase of the methane ICE illustrated in FIGS. 5A-5B results in rapidconvergence between master sensor and node sensor data in tool parameterspace even prior to applying a weighting factor to perform anycompensation on the master sensor responses (cf. step 406 in method400).

FIG. 5C illustrates a chart 500C with a data cross-correlation betweenthe master sensor and the node sensor illustrated in FIG. 5A.Accordingly, the abscissae 553 in chart 500C correspond to thecompensated master sensor responses in tool parameter space. Thecompensated master sensor responses are obtained using a method such asmethod 400, including step 406. More specifically, data in the abscissaeof FIG. 5C may be obtained by performing mathematical operations such asincluded in Eq. 1 with a suitable weighting factor, C. The ordinates 552in chart 500C correspond to the node sensor responses in tool parameterspace.

FIGS. 6A-6C illustrate a cross-sensor linearization procedure for asensor channel including a Gas-Oil-Ratio (GOR) ICE, according to someembodiments. FIGS. 6A-6C illustrate a scenario in which the mastersensor and node sensor are among different calibration batches. Thesensors are configured in the same way, and the selected ICE cores (GORICE in this case) are fabricated with the same design.

FIG. 6A illustrates chart 600A with a master sensor spectral response602 and a node sensor spectral response 604. Chart 600A includeswavelength in the abscissae and transmission in the ordinates. Spectralresponses 602 and 604 may be used in R_(n,m) for the calculation of thesensor response in synthetic parameter space (cf. Eq. (2) above).

FIG. 6B illustrates chart 600B with a data cross-correlation between themaster sensor and the node sensor illustrated in FIG. 6A. Accordingly,the abscissae 651 in chart 600B correspond to the master sensorresponses in tool parameter space. The ordinates 652 in chart 600Bcorrespond to the node sensor responses in tool parameter space. Themultiple data points in chart 600B correspond to a reduced set ofreference fluids, and are clustered as detailed above in reference toFIGS. 5A-5C. Accordingly, data clusters 601 a-c correspond to GOL33;data clusters 603 a-c correspond to GOL13; data clusters 605 a-ccorrespond to H₂O (water); data clusters 607 a-c correspond to toluene;data clusters 609 a-c correspond to 1-5 pentanediol (PEN); data clusters611 a-c correspond to dodecane (DOD); and data clusters 613 a-ccorrespond to N₂ (nitrogen). FIG. 6B Cross-sensor ICE data correlationcannot be modeled with a single linear function without compensation.

FIG. 6C illustrates a chart 600C with a data cross-correlation betweenthe master sensor and the node sensor illustrated in FIG. 6A.Accordingly, the abscissae 653 in chart 600C correspond to thecompensated master sensor responses in tool parameter space. Theordinates 652 in chart 600C correspond to the node sensor responses intool parameter space. In chart 600C, the compensated master sensorresponse has demonstrated better linear correlation with node sensorresponse in this scenario, as compared to chart 600B.

FIGS. 7A-7C illustrate a cross-sensor linearization procedure for asensor channel including an Aromatics (ARO) ICE, according to someembodiments. FIGS. 7A-7C illustrate a scenario in which the selected ICEelements (e.g., an ICE for measuring aromatics—‘aromatics ICE’—in thiscase) on master sensor and node sensors are not only from differentcalibration batches, but also from the different designs.

FIG. 7A illustrates chart 700A with a master sensor spectral response702 and a node sensor spectral response 704. Chart 700A includeswavelength in the abscissae and transmission in the ordinates. Spectralresponses 702 and 704 may be used in R_(n,m) for the calculation of thesensor response in synthetic parameter space (cf. Eq. (2) above).

FIG. 7B illustrates chart 700B with a data cross-correlation between themaster sensor and the node sensor illustrated in FIG. 7A. Accordingly,the abscissae 751 in chart 700B correspond to the master sensorresponses in tool parameter space. The ordinates 752 in chart 700Bcorrespond to the node sensor responses in tool parameter space. Themultiple data points in chart 700B correspond to a reduced set ofreference fluids, and are clustered as detailed above in reference toFIGS. 5A-5C. Accordingly, data clusters 701 a-c correspond to GOL33;data clusters 703 a-c correspond to GOL13; data clusters 705 a-ccorrespond to H₂O (water); data clusters 707 a-c correspond to toluene;data clusters 709 a-c correspond to 1-5 pentanediol (PEN); data clusters711 a-c correspond to dodecane (DOD); and data clusters 713 a-ccorrespond to N₂ (nitrogen).

Although sensors have the same number of nominal elements inconfiguration, the direct data correlation without spectral correctionappears to be non-linear again on the given reference fluids. Forexample, reference fluids associated with data clusters 705 c and 709 ahave similar master sensor responses 751, but completely different nodesensor responses 752. Likewise, reference fluids associated with dataclusters 711 a and 709 c have similar master sensor responses 751 butdifferent node sensor responses 752. Moreover, reference fluidsassociated with data clusters 707 a, 707 b, and 707 c have differentmaster sensor responses 751 but similar node sensor responses 752.

FIG. 7C illustrates a chart 700C with a data cross-correlation betweenthe master sensor and the node sensor illustrated in FIG. 7A.Accordingly, the abscissae 753 in chart 700C correspond to thecompensated master sensor responses in tool parameter space. Thecompensated master sensor responses are obtained using a method such asmethod 400, including step 406. More specifically, data in the abscissaeof FIG. 7C may be obtained by performing mathematical operations such asincluded in Eq. (1) with a suitable weighting factor, C. The ordinates752 in chart 700C correspond to the node sensor responses in toolparameter space. The significantly improved cross-sensor ICE datalinearization is also achieved in this case using the invented method.

FIGS. 8A-8C illustrate a cross-sensor linearization procedure for asensor channel including an ICE for measuring saturates, or ‘saturates(SAT) ICE’, according to some embodiments. FIGS. 8A-8C illustrate ascenario for cross-sensor ICE data linearization wherein the calibrationbatch, the sensor configuration and the optical element design (SAT ICEin this example) are all different between master and node elements.

FIG. 8A illustrates chart 800A with a master sensor spectral response802 and a node sensor spectral response 804. Chart 800A includeswavelength in the abscissae and transmission in the ordinates. Spectralresponses 802 and 804 may be used in R_(n,m) for the calculation of thesensor response in synthetic parameter space (cf. Eq. (2) above).

FIG. 8B illustrates chart 800B with a data cross-correlation between themaster sensor and the node sensor illustrated in FIG. 8A. Accordingly,the abscissae 851 in chart 800B correspond to the master sensorresponses in tool parameter space. The ordinates 852 in chart 800Bcorrespond to the node sensor responses in tool parameter space. Themultiple data points in chart 800B correspond to a reduced set ofreference fluids, and are clustered as detailed above in reference toFIGS. 5A-5C. Data clusters 801 a-c correspond to GOL33; data clusters803 a-c correspond to GOL13; data clusters 805 a-c correspond to H₂O(water); data clusters 807 a-c correspond to toluene; data clusters 809a-c correspond to 1-5 pentanediol (PEN); data clusters 811 a-ccorrespond to dodecane (DOD); and data clusters 813 a-c correspond to N₂(nitrogen).

FIG. 8C illustrates a chart 800C with a data cross-correlation betweenthe master sensor and the node sensor illustrated in FIG. 8A.Accordingly, the abscissae 853 in chart 800C correspond to thecompensated master sensor responses in tool parameter space. Thecompensated master sensor responses are obtained using a method such asmethod 400, including step 406. More specifically, data in the abscissaeof FIG. 8C may be obtained by performing mathematical operations such asincluded in Eq. (1) with a suitable weighting factor, C. The ordinates852 in chart 800C correspond to the node sensor responses in toolparameter space. FIG. 8C indicates that a reasonably good linearcorrelation can be generated using linearization methods consistent withthe present disclosure. Accordingly, methods as disclosed herein providea robust approach for standardization of sensor data in tool parameterspace for a wide variety of applications.

The linear correlation between compensated master sensor responses andnode sensor responses in charts 500C, 600C, 700C, and 800C are expressedmathematically by linear coefficients ‘k’ and ‘b’, (cf. Eq. 3). Asillustrated, the coefficients ‘k’ and ‘b’ and the associated weightingcoefficient ‘C’ in calculating compensated master sensor response (cf.Eq. 1) depend on the optical element and the particular sensor pairsbeing considered. That is, in some embodiments the coefficients ‘k’, ‘b’and ‘C’ may differ between chart 500C, chart 600C, chart 700C, and chart800C (e.g., a methane ICE in FIGS. 5A-5C, an ICE for measuringGas-to-Oil-Ratio ‘GOR ICE’ in FIGS. 6A-6C, an aromatics ICE in FIGS.7A-7C, and a saturates ICE in FIGS. 8A-8C, respectively). For differentmaster-node sensor pairs the coefficients ‘k’, ‘b’ and ‘C’ may alsodiffer even with same nominal design of a methane ICE, or a GOR ICE, oran aromatics ICE, or a saturates ICE.

FIG. 9 illustrates a schematic flowchart including steps in a method 900to be implemented for cross-sensor linearization and its application forimproving reverse transformation and fluid characterization, accordingto some embodiments. Method 900 may be performed by a computer devicehaving a memory and a processor (e.g., computer 140, memory 142, andprocessor 144, cf. FIG. 1). The memory may store commands that, whenexecuted by the processor, cause the computer to perform at least someof the steps in method 900. Methods consistent with method 900 mayinclude at least one but not all of the steps in method 900, performedin any order. Furthermore, methods consistent with the scope of method900 may include at least some of the steps in method 900 performedoverlapping in time, or even simultaneously.

Methods consistent with method 900 may include measuring referencefluids with a measurement system using an optical sensor having aplurality of optical elements (e.g., measurement system 102 and opticalelements 104 a-n, cf. FIG. 1). In some embodiments, the plurality ofoptical elements in method 400 may correspond to the same opticalsensor, or may belong to different optical sensors. Accordingly, theplurality of optical elements in method 400 may be selected within thesame fabrication batch, among the different fabrication batches, withinthe same optical element design, among different optical elementdesigns, within the same sensor configuration or among different sensorconfigurations. In some embodiments, the measurement system in method400 may include a reverse transformation or a forward transformationbetween sensor responses in a tool parameter space and sensor responsesin a synthetic parameter space (e.g., tool parameter space 201,synthetic parameter space 202, reverse transformation 203, and forwardtransformation 205).

Embodiments consistent with method 900 reduce calibration costs bylinearizing cross-sensor correlation. In method 900 and embodimentsconsistent with the method 900, only a small number of master sensors,which could consist of the selected single or multiple representativesensors from each generation of sensors with same configuration andoptical element design, are calibrated on a full-set of referencefluids. The remaining number of node sensors are calibrated on areduced-set of reference fluids. In some embodiments, the reduced set ofreference fluids is a sub-set of the full-set of reference fluids.Method 900 is oriented to obtain a linear mapping, which relatescompensated master sensor response for each optical element to a nodesensor response in a tool parameter space based on the reduced-set ofreference fluids (cf. chart 500C, 600C, 700C, and 800C, above). Further,methods consistent with method 900 include obtaining node sensorresponses on additional reference fluids from the linear model justfound. Accordingly, methods consistent with method 900 simplifycalibration procedures for node sensor by reducing the measurements onreference fluids.

Method 900 describes the procedure to generate node sensor responses insynthetic and tool parameter space on additional reference fluids withchannel-by-channel linearization as disclosed herein. Step 902 includesidentifying a pair of a master sensor and a node sensor sharing areduced set of reference fluids. Step 904 includes determining adifference between the responses of the node sensor and the mastersensor in the synthetic parameter space for the reduced set of referencefluids to calculate compensated master sensor response in tool parameterspace. Step 906 includes correlating values for a compensated mastersensor response with values for the measured node sensor response. Step908 includes determining a node sensor response for additional referencefluids in a tool parameter space using channel-by-channel linearizationmodels with the compensated master sensor response as input.

Step 908 is applied to new data using the models developed on thetraining data of reduced-set of reference fluids. The additionalreference fluids as new data may include live oil sample and methane,the important representatives of petroleum fluids. Since the mastersensor has measurements of full-set reference fluids available, and thedifference of synthetic node sensor and master sensor response can becalculated in synthetic parameter space, the calculation of pseudo nodesensor response is straightforward using the same equations describedabove (cf. Eqs. 1-3).

Step 910 includes determining a reverse transformation using the nodesensor response for a complete set of reference fluids. Step 912includes adjusting a response from an optical sensor in a wellbore usingthe reverse transformation to obtain a characteristic of a wellborefluid from the adjusted response. Step 914 includes modifying operationparameters of drilling or well testing and sampling according to thecharacteristic of the wellbore fluid.

FIG. 10 illustrates a flowchart including steps in a method 1000 as apre-processing procedure for cross-sensor linearization according tosome embodiments, to generate matched data pairs of master and nodesensors in tool parameter space. Method 1000 may be performed by acomputer device having a memory and a processor (e.g., computer 140,memory 142, and processor 144, cf. FIG. 1). The memory may storecommands that, when executed by the processor, cause the computer toperform at least some of the steps in method 1000. Methods consistentwith method 1000 may include at least one but not all of the steps inmethod 1000, performed in any order. Furthermore, methods consistentwith the scope of method 1000 may include at least some of the steps inmethod 1000 performed overlapping in time, or even simultaneously.

Methods consistent with method 1000 may include measuring referencefluids with a measurement system using an optical sensor having aplurality of optical elements (e.g., measurement system 102 and opticalelements 104 a-n, cf. FIG. 1). In some embodiments, the plurality ofoptical elements in method 1000 may correspond to the same opticalsensor, or may belong to different optical sensors. Accordingly, theplurality of optical elements in method 1000 may be selected within thesame fabrication batch, among the different fabrication batches, withinthe same optical element design, among different optical elementdesigns, within the same sensor configuration or among different sensorconfigurations. In some embodiments, the measurement system in method1000 may include a reverse transformation or a forward transformationbetween sensor responses in a tool parameter space and sensor responsesin a synthetic parameter space (e.g., tool parameter space 201,synthetic parameter space 202, reverse transformation 203, and forwardtransformation 205).

Method 1000 includes matching data pairs from the master sensor and thenode sensor to a reduced-set of reference fluids. The reduced-set ofreference fluids may include water, nitrogen, one or two typical deadoils, toluene, pentanediol and dodecane, which are safe to takemeasurements under the specified temperature and pressure settings. Step1002 includes collecting master sensor data for a plurality of referencefluids at a plurality of temperature and pressure settings and for aplurality of channels. Step 1004 includes collecting node sensor datafor the reduced set of reference fluids from the plurality of referencefluids at a plurality of temperature and pressure settings.

Step 1006 includes sorting measured master and node sensor responses oneach reference fluid in the reduced set at each stabilized temperatureand pressure setting. Step 1008 includes truncating data pairs to thesame number of sample points under each condition according to whichdata size is smaller. Step 1010 includes combining multi-fluid datapairs to form a complete data set.

FIG. 11 illustrates a flowchart including steps in a method 1100 forcross-sensor linearization with use of a two-dimensional temperature andpressure interpolation scheme for correcting synthetic sensor responseand generating optimized model coefficients on the training fluids,according to some embodiments. Method 1100 may be performed by acomputer device having a memory and a processor (e.g., computer 140,memory 142, and processor 144, cf. FIG. 1). The memory may storecommands that, when executed by the processor, cause the computer toperform at least some of the steps in method 1100. Methods consistentwith method 1100 may include at least one but not all of the steps inmethod 1100, performed in any order. Furthermore, methods consistentwith the scope of method 1100 may include at least some of the steps inmethod 1100 performed overlapping in time, or even simultaneously.

Methods consistent with method 1100 may include measuring referencefluids with a measurement system using an optical sensor having aplurality of optical elements (e.g., measurement system 102 and opticalelements 104 a-n, cf. FIG. 1). In some embodiments, the plurality ofoptical elements in method 1100 may correspond to the same opticalsensor, or may belong to different optical sensors. Accordingly, theplurality of optical elements in method 1100 may be selected within thesame fabrication batch, among the different fabrication batches, withinthe same optical element design, among different optical elementdesigns, within the same sensor configuration or among different sensorconfigurations. In some embodiments, the measurement system in method1100 may include a reverse transformation or a forward transformationbetween sensor responses in a tool parameter space and sensor responsesin a synthetic parameter space (e.g., tool parameter space 201,synthetic parameter space 202, reverse transformation 203, and forwardtransformation 205).

The flowchart in FIG. 11 starts with steps to calculate the differencebetween node and master sensor responses in synthetic parameter space(S_(n) and S_(m) in Eq. (1)) on the reduced-set of reference fluids(steps 1102 to 1106) using Eq. (2) and two-dimensional interpolation.Synthetic sensor responses obtained with Eq. (2) are representatives of‘ideal’ data points with fluid spectroscopy data averaged over a largenumber of measurements around each specified temperature and pressurecombination setting. After the responses of each optical element at 12combination setting points (3 temperatures and 4 pressures) arecalculated for each reference fluid, the data relationship between thesynthetic optical responses and the ideal temperatures and pressures canbe organized in the format of 3 by 4 matrices as the given points fortwo-dimensional interpolation in simulating the synthetic response ofthe same optical element with other within-range temperatures andpressures as inputs.

Step 1102 includes determining an estimated value for a node sensorresponse on each fluid at ideal setting points in synthetic parameterspace from Eq. (2), and using two-dimensional interpolation withactually measured temperature and pressure in tool parameter space asinputs to correct signal variation. Step 1102 corrects the drift ofsynthetic signals of node sensor in response to slight variations intemperature and pressure settings from ideal setting values duringmeasurement. Step 1104 includes determining an estimated value for amaster sensor response under the same conditions of Step 1102 insynthetic parameter space from Eq. (2), and using two-dimensionaltemperature and pressure interpolation to correct signal drift due tovariation in actual temperature and pressure measurements which mayendure slight change around the ideal setting values. Step 1106 includesdetermining a difference between the estimated values for a node sensorresponse and the estimated value for a master sensor response. Step 1108includes determining a set of cross-sensor linearized model coefficients(e.g., ‘C’, ‘k’, and ‘b’ in Eq. (1) and Eq. (3)) in an optimizationloop. In some embodiments, step 1108 includes selecting the set ofcoefficients ‘C’, ‘k’ and ‘b’ that result in the best linear fit (cf.Eq. (3)). Step 1108 includes determining a set of cross-sensorlinearized model coefficients in an exhaustive searching or optimizationloop through multi-iteration training.

When the master sensor and the node sensor have different configurationor element design, a particular element response of the node sensor maybe simulated with a different nominal element response of the mastersensor (i.e., a Methane ICE response of the node sensor may be bettersimulated with a GOR ICE response of the master sensor). Step 1110includes adjusting master sensor channel selection to simulate aparticular channel response of the node sensor with different elementdesign, and re-calculating the compensated master sensor response andre-determining a set of coefficients of ‘C’, ‘k’, and ‘b’. Accordingly,step 1110 may include adjusting the master sensor response from a mastersensor channel to simulate a node sensor response from a node sensorchannel wherein the master sensor channel may be the same, or different,than the node sensor channel. In general, the choice of master-sensorchannel and node sensor channel pairs to be correlated (e.g. abscissaeand ordinates in FIGS. 5B,C, FIGS. 6B,C, FIGS. 7B,C, and FIGS. 8B,C) isbased on which channel correlation results in the best, or better,linear correlation between the data from the two sensor channels (i.e.,the master sensor channel and the node sensor channel). Accordingly,method 1100 may further include adjusting a master sensor channelselection from a master sensor to simulate a node sensor channelresponse from a node sensor wherein the master sensor channel has thesame or different nominal element as the node sensor channel.

Step 1112 includes storing at least one set of cross-sensor linearizedmodel coefficients for at least one node sensor channel. Step 1112 savesthe best set of cross-sensor linearized model coefficients for each nodesensor channel based on the reduced set of reference fluids and appliesthem to simulate the node sensor responses of additional referencefluids to be described in FIG. 12.

FIG. 12 illustrates a flowchart including steps in a method 1200 forcross-sensor linearization by estimating and including a node sensorresponse for an additional set of reference fluids for robust reversetransformation, according to some embodiments. Method 1200 may beperformed by a computer device having a memory and a processor (e.g.,computer 140, memory 142, and processor 144, cf. FIG. 1). The memory maystore commands that, when executed by the processor, cause the computerto perform at least some of the steps in method 1200. Methods consistentwith method 1200 may include at least one but not all of the steps inmethod 1200, performed in any order. Furthermore, methods consistentwith the scope of method 1200 may include at least some of the steps inmethod 1200 performed overlapping in time, or even simultaneously.

Methods consistent with method 1200 may include measuring referencefluids with a measurement system using an optical sensor having aplurality of optical elements (e.g., measurement system 102 and opticalelements 104 a-n, cf. FIG. 1). In some embodiments, the plurality ofoptical elements in method 1200 may correspond to the same opticalsensor, or may belong to different optical sensors. Accordingly, theplurality of optical elements in method 1200 may be selected within thesame fabrication batch, among different fabrication batches, within thesame optical element design, among different optical element designs,within the same sensor configuration or among different sensorconfigurations. In some embodiments, the measurement system in method1200 may include a reverse transformation or a forward transformationbetween sensor responses in a tool parameter space and sensor responsesin a synthetic parameter space (e.g., tool parameter space 201,synthetic parameter space 202, reverse transformation 203, and forwardtransformation 205).

Step 1202 includes determining an estimated node sensor response insynthetic parameter space for an extended set of reference fluids withuse of Eq. (2) and two-dimensional temperature and pressureinterpolation. Step 1204 includes determining a master sensor responsein synthetic parameter space for an extended set of reference fluids.Step 1206 includes determining a compensated master sensor response intool parameter space according to a predetermined weighting factor. Atstep 1206, the compensated master sensor response on the additional setof reference fluids is calculated in Eq. (1) with use of eachpre-determined weighting factor value, C, channel by channel. Step 1208includes determining an estimated node sensor response through Eq. (3)with use of each set of pre-determined coefficients ‘k’ and ‘b’ channelby channel. Step 1210 includes determining a reverse transformationusing the estimated node sensor response in tool parameter space for acomplete set of reference fluids as training inputs. In someembodiments, step 1210 includes determining node sensor responses insynthetic parameter for the same set of reference fluids as trainingoutputs. Step 1212 includes adjusting a response from an optical sensorin a wellbore using the reverse transformation to obtain acharacteristic of a wellbore fluid from the adjusted response. Step 1214includes modifying operation parameters of drilling or well testing andsampling according to the characteristic of the wellbore fluid.

FIG. 13 is a drilling system 1300 configured to use a calibrated opticalsensor for modifying a drilling parameter or configuration in ameasurement-while-drilling (MWD) and a logging-while-drilling (LWD)operation, according to some embodiments. Boreholes may be created bydrilling into the earth 1302 using the drilling system 1300. Thedrilling system 1300 may be configured to drive a bottom hole assembly(BHA) 1304 positioned or otherwise arranged at the bottom of a drillstring 1306 extended into the earth 1302 from a derrick 1308 arranged atthe surface 1310. The derrick 1308 includes a Kelly 1312 and a travelingblock 1313 used to lower and raise the Kelly 1312 and the drill string1306.

The BHA 1304 may include a drill bit 1314 operatively coupled to a toolstring 1316 which may be moved axially within a drilled wellbore 1318 asattached to the drill string 1306. During operation, the drill bit 1414penetrates the earth 1302 and thereby creates the wellbore 1318. The BHA1404 provides directional control of the drill bit 1314 as it advancesinto the earth 1302. The tool string 1316 can be semi-permanentlymounted with various measurement tools (not shown) such as, but notlimited to, measurement-while-drilling (MWD) and logging-while-drilling(LWD) tools, that may be configured to take downhole measurements ofdrilling conditions. In other embodiments, the measurement tools may beself-contained within the tool string 1316, as shown in FIG. 13.

Fluid or “mud” from a mud tank 1320 may be pumped downhole using a mudpump 1322 powered by an adjacent power source, such as a prime mover ormotor 1324. The mud may be pumped from the mud tank 1320, through astand pipe 1326, which feeds the mud into the drill string 1306 andconveys the same to the drill bit 1314. The mud exits one or morenozzles arranged in the drill bit 1314 and in the process cools thedrill bit 1314. After exiting the drill bit 1314, the mud circulatesback to the surface 1310 via the annulus defined between the wellbore1318 and the drill string 1306, and in the process returns drillcuttings and debris to the surface. The cuttings and mud mixture arepassed through a flow line 1328 and are processed such that a cleanedmud is returned down hole through the stand pipe 1326 once again.

The BHA 1304 may further include a downhole tool 1330 that may besimilar to the downhole tools described herein. More particularly, thedownhole tool 1330 may have a calibrated optical sensor arrangedtherein, and the downhole tool 1330 may have been calibrated prior tobeing introduced into the wellbore 1318 using the tool validationtesting generally described herein. Moreover, prior to being introducedinto the wellbore 1318, the downhole tool 1330 may have been optimizedby generally following method 400 of FIG. 4. In some embodiments,downhole tool 1330 is configured to perform at least one of the stepsdescribed above in any one of methods 900, 1000, 1100, and 1200.

FIG. 14, illustrates a wireline system 1400 that may employ one or moreprinciples of the present disclosure. In some embodiments, wirelinesystem 1400 may be configured to use a calibrates optical sensor duringformation testing and sampling. After drilling of wellbore 1318 iscomplete, it may be desirable to know more details of types of formationfluids and the associated characteristics through sampling with use ofwireline formation tester. System 1400 may include a downhole tool 1402that forms part of a wireline logging operation that can include one ormore optical sensors 1404, as described herein, as part of a downholemeasurement tool. System 1400 may include the derrick 1308 that supportsthe traveling block 1313. Wireline logging tool 1402, such as a probe orsonde, may be lowered by wireline or logging cable 1406 into theborehole 1318. Tool 1402 may be lowered to the bottom of the region ofinterest and subsequently pulled upward at a substantially constantspeed. Tool 1402 may be configured to measure fluid properties of thewellbore fluids, and any measurement data generated by downhole tool1402 and its associated optical sensors 1404 can be communicated to asurface logging facility 1408 for storage, processing, and/or analysis.Logging facility 1408 may be provided with electronic equipment 1410,including processors for various types of signal processing. In someembodiments, downhole tool 1402 and logging facility 1408 are configuredto perform at least one of the steps described above in any one ofmethods 400, 900, 1000, 1100, and 1200.

Embodiments disclosed herein include:

A. A method that includes obtaining a plurality of master sensorresponses with a master sensor in a set of training fluids, obtaining aplurality of node sensor responses with a plurality of node sensors inthe set of training fluids, finding a linear correlation between acompensated master data set and a node data set for the set of trainingfluids, generating a plurality of node sensor responses in a toolparameter space from the compensated master data set on a set ofapplication fluids, obtaining a reverse transformation based on theplurality of node sensor responses in a complete set of calibrationfluids, the reverse transformation transforming each node sensorresponse from a tool parameter space to a synthetic parameter space,obtaining fluid characteristics with synthetic fluid predictive modelsusing reverse-transformed inputs from at least one of the node sensorresponses to a fluid measurement, and modifying operation parameters ofa drilling or a well testing and sampling system according to the fluidcharacteristics, wherein the complete set of calibration fluidscomprises the set of training fluids and the set of application fluids.

B. A method that includes determining an value for a node sensorresponse in synthetic parameter space using a two-dimensionaltemperature and pressure interpolation with given node sensor responsesat specified temperatures and pressures, determining an value for amaster sensor response in synthetic parameter space using thetwo-dimensional temperature and pressure interpolation with given mastersensor response at specified temperatures and pressures, determining adifference between the value for a node sensor response and the valuefor a master sensor response, determining a set of cross-sensorlinearized model coefficients in an optimization loop, adjusting amaster sensor channel selection to simulate a channel response of thenode sensor, obtaining a reverse transformation using the simulatedchannel responses of the node sensor, and modifying operation parametersof a drilling or a well testing and sampling system according to a fluidcharacteristic obtained with a synthetic fluid predictive model usingnode sensor responses as input to the reverse transformation.

C. A method that includes introducing a tool into a wellbore drilledinto one or more subterranean formations, the tool having beenpreviously calibrated for operation by obtaining a plurality of mastersensor responses with a master sensor in a set of training fluids,obtaining a plurality of node sensor responses with a plurality of nodesensors in the set of training fluids, each of the plurality of nodesensors and the master sensor including an optical element, finding alinear correlation between a compensated master data set and a node dataset for the set of training fluids, generating a plurality of nodesensor responses in a tool parameter space from the compensated masterdata set on a set of application fluids, and obtaining a reversetransformation based on the plurality of node sensor responses in acomplete set of calibration fluids, wherein the complete set ofcalibration fluids comprises the set of training fluids and the set ofapplication fluids, determining a fluid characteristic from theplurality of node sensor responses in the synthetic parameter spaceusing the reverse transformation and a synthetic fluid predictive model,and modifying operation parameters of a drilling or a well testing andsampling according to the fluid characteristic.

Each of embodiments A, B, and C may have one or more of the followingadditional elements in any combination: Element 1: further comprisingselecting a weighting factor to compensate the master sensor responseswith the node sensor responses according to the linear correlationbetween the compensated master data set and the node data set. Element2: wherein selecting the weighting factor comprises selecting aweighting factor that results in a high linear correlation between thecompensated master data set and the node data set, wherein the highlinear correlation indicates a low data transformation error. Element 3:wherein selecting the weighting factor comprises determining a set ofcross-sensor linearized coefficients comprising the weighting factor foreach channel pair, using an exhaustive searching loop throughmulti-iteration training Element 4: further comprising selecting themaster sensor and at least one of the plurality of node sensors from twosensors having a same design, two sensors having a same configuration,and two sensors from a fabrication batch. Element 5: further comprisingselecting the master sensor and at least one of the plurality of nodesensors from different fabrication batches, and from two sensors havinga same design and having a same configuration. Element 6: furthercomprising selecting the master sensor and at least one of the pluralityof node sensors from different fabrication batches having a differentdesign, and with a same number of elements having the same denomination.Element 7: further comprising selecting the master sensor and at leastone of the plurality of node sensors from different designs, fromdifferent configurations, and originating from different fabricationbatches. Element 8: further comprising truncating a master data set to asame number of samples as a node data set, wherein each sample in themaster data set comprises a measurement having a temperature setting andpressure setting similar to a temperature setting and a pressure settingof at least one measurement in the node data set. Element 9: whereinfinding a linear correlation between a compensated master data and thenode data set comprises applying a weight factor to a difference betweena synthetic node sensor response and a synthetic master sensor responsefor a reference fluid selected from the set of training fluids, andadding the weighted difference to a master sensor response measured fromthe reference fluid. Element 10: further comprising determining at leastone of a node sensor response and a master sensor response in thesynthetic parameter space with a dot product of a fluid spectralresponse vector and a convolved spectral response vector for one of theat least one node sensor or the master sensor. Element 11: furthercomprising obtaining fluid characteristics with a synthetic fluidpredictive model using the reverse transformed inputs from at least oneof the node sensor responses to a fluid measurement. Element 12: whereinobtaining a plurality of node sensor responses with a plurality of nodesensors on the set of training fluids comprises measured and simulatednode sensor responses from reference fluids at broad ranges oftemperature settings and pressure settings. Element 13: furthercomprising collecting optical responses from a plurality of petroleumfluids with known characteristics using the selected master sensor,generating a plurality of synthetic node sensor responses associatedwith the plurality of petroleum fluids using the reverse transformationwith cross-sensor linearized node sensor inputs in tool parameter space,and calibrating a fluid characterization model using the plurality ofsynthetic node sensor responses.

Element 14: wherein determining the value for a node sensor response anddetermining the value for a master sensor response comprises varyingtemperature and pressure conditions for a plurality of node sensorresponses and master sensor responses. Element 16: wherein adjusting themaster sensor channel selection to simulate a channel response of thenode sensor comprises identifying a set of cross-sensor linearizedcoefficients for a node sensor channel based on a plurality of trainingfluids, and obtaining the channel response of the node sensor on aplurality of application fluids with the set of cross-sensor linearizedmodel coefficients. Element 17: wherein obtaining a reversetransformation using the simulated channel responses of the node sensorcomprises combining the node sensor response on a plurality of trainingfluids and a plurality of application fluids to develop the reversetransformation model with a neural network. Element 18: furthercomprising adjusting a master sensor channel selection from a mastersensor to simulate a node sensor channel response from a node sensor.Element 19: wherein the master sensor channel has the same or differentnominal element as the node sensor channel.

Element 20: wherein obtaining a plurality of node sensor responses witha plurality of node sensors in the set of training fluids during thetool calibration comprises determining a temperature setting and apressure setting of the reduced set of training fluids according to atemperature setting and a pressure setting of the master set of trainingfluids. Element 21: further comprising, during the tool calibration,selecting one of the plurality of master sensors and one of theplurality of node sensors from two sensors having at least one ofdifferent designs, different configurations, or different fabricationbatches.

By way of non-limiting example, exemplary combinations applicable to A,B, and C include: Element 1 with Element 2; Element 1 with Element 2;and Element 18 with Element 19.

Therefore, the disclosed systems and methods are well adapted to attainthe ends and advantages mentioned as well as those that are inherenttherein. The particular embodiments disclosed above are illustrativeonly, as the teachings of the present disclosure may be modified andpracticed in different but equivalent manners apparent to those skilledin the art having the benefit of the teachings herein. Furthermore, nolimitations are intended to the details of construction or design hereinshown, other than as described in the claims below. It is thereforeevident that the particular illustrative embodiments disclosed above maybe altered, combined, or modified and all such variations are consideredwithin the scope of the present disclosure. The systems and methodsillustratively disclosed herein may suitably be practiced in the absenceof any element that is not specifically disclosed herein and/or anyoptional element disclosed herein. While compositions and methods aredescribed in terms of “comprising,” “containing,” or “including” variouscomponents or steps, the compositions and methods can also “consistessentially of” or “consist of” the various components and steps. Allnumbers and ranges disclosed above may vary by some amount. Whenever anumerical range with a lower limit and an upper limit is disclosed, anynumber and any included range falling within the range is specificallydisclosed. In particular, every range of values (of the form, “fromabout a to about b,” or, equivalently, “from approximately a to b,” or,equivalently, “from approximately a-b”) disclosed herein is to beunderstood to set forth every number and range encompassed within thebroader range of values. Also, the terms in the claims have their plain,ordinary meaning unless otherwise explicitly and clearly defined by thepatentee. Moreover, the indefinite articles “a” or “an,” as used in theclaims, are defined herein to mean one or more than one of the elementthat it introduces. If there is any conflict in the usages of a word orterm in this specification and one or more patent or other documentsthat may be incorporated herein by reference, the definitions that areconsistent with this specification should be adopted.

As used herein, the phrase “at least one of” preceding a series ofitems, with the terms “and” or “or” to separate any of the items,modifies the list as a whole, rather than each member of the list (i.e.,each item). The phrase “at least one of” allows a meaning that includesat least one of any one of the items, and/or at least one of anycombination of the items, and/or at least one of each of the items. Byway of example, the phrases “at least one of A, B, and C” or “at leastone of A, B, or C” each refer to only A, only B, or only C; anycombination of A, B, and C; and/or at least one of each of A, B, and C.

What is claimed is:
 1. A method, comprising: obtaining a plurality ofmaster sensor responses with a master sensor in a set of trainingfluids; obtaining a plurality of node sensor responses with a pluralityof node sensors in the set of training fluids; finding a linearcorrelation between a compensated master data set and a node data setfor the set of training fluids; generating a plurality of node sensorresponses in a tool parameter space from the compensated master data seton a set of application fluids; obtaining a reverse transformation basedon the plurality of node sensor responses in a complete set ofcalibration fluids, the reverse transformation transforming each nodesensor response from a tool parameter space to a synthetic parameterspace; obtaining fluid characteristics with synthetic fluid predictivemodels using reverse-transformed inputs from at least one of the nodesensor responses to a fluid measurement; and modifying operationparameters of a drilling or a well testing and sampling system accordingto the fluid characteristics, wherein the complete set of calibrationfluids comprises the set of training fluids and the set of applicationfluids.
 2. The method of claim 1, further comprising: selecting aweighting factor to compensate the master sensor responses with the nodesensor responses according to the linear correlation between thecompensated master data set and the node data set.
 3. The method ofclaim 2, wherein selecting the weighting factor comprises selecting aweighting factor that results in a high linear correlation between thecompensated master data set and the node data set, wherein the highlinear correlation indicates a low data transformation error.
 4. Themethod of claim 2, wherein selecting the weighting factor comprisesdetermining a set of cross-sensor linearized coefficients comprising theweighting factor for each channel pair, using an exhaustive searchingloop through multi-iteration training.
 5. The method of claim 1, furthercomprising selecting the master sensor and at least one of the pluralityof node sensors from two sensors having a same design, two sensorshaving a same configuration, and two sensors from a fabrication batch.6. The method of claim 1, further comprising selecting the master sensorand at least one of the plurality of node sensors from differentfabrication batches, and from two sensors having a same design andhaving a same configuration.
 7. The method of claim 1, furthercomprising selecting the master sensor and at least one of the pluralityof node sensors from different fabrication batches having a differentdesign, and with a same number of elements having the same denomination.8. The method of claim 1, further comprising selecting the master sensorand at least one of the plurality of node sensors from differentdesigns, from different configurations, and originating from differentfabrication batches.
 9. The method of claim 1, further comprisingtruncating a master data set to a same number of samples as a node dataset, wherein each sample in the master data set comprises a measurementhaving a temperature setting and pressure setting similar to atemperature setting and a pressure setting of at least one measurementin the node data set.
 10. The method of claim 1, wherein finding alinear correlation between a compensated master data and the node dataset comprises applying a weight factor to a difference between asynthetic node sensor response and a synthetic master sensor responsefor a reference fluid selected from the set of training fluids, andadding the weighted difference to a master sensor response measured fromthe reference fluid.
 11. The method of claim 1, further comprisingdetermining at least one of a node sensor response and a master sensorresponse in the synthetic parameter space with a dot product of a fluidspectral response vector and a convolved spectral response vector forone of the at least one node sensor or the master sensor.
 12. The methodof claim 1, further comprising obtaining fluid characteristics with asynthetic fluid predictive model using the reverse transformed inputsfrom at least one of the node sensor responses to a fluid measurement.13. The method of claim 1, wherein obtaining a plurality of node sensorresponses with a plurality of node sensors on the set of training fluidscomprises measured and simulated node sensor responses from referencefluids at broad ranges of temperature settings and pressure settings.14. The method of claim 1, further comprising: collecting opticalresponses from a plurality of petroleum fluids with knowncharacteristics using the selected master sensor; generating a pluralityof synthetic node sensor responses associated with the plurality ofpetroleum fluids using the reverse transformation with cross-sensorlinearized node sensor inputs in tool parameter space; and calibrating afluid characterization model using the plurality of synthetic nodesensor responses.
 15. A method, comprising: determining a value for anode sensor response in synthetic parameter space using atwo-dimensional temperature and pressure interpolation with given nodesensor responses at specified temperatures and pressures; determining avalue for a master sensor response in synthetic parameter space usingthe two-dimensional temperature and pressure interpolation with givenmaster sensor response at specified temperatures and pressures;determining a difference between the value for a node sensor responseand the value for a master sensor response; determining a set ofcross-sensor linearized model coefficients in an optimization loop;adjusting a master sensor channel selection to simulate a channelresponse of the node sensor; obtaining a reverse transformation usingthe simulated channel responses of the node sensor; and modifyingoperation parameters of a drilling or a well testing and sampling systemaccording to a fluid characteristic obtained with a synthetic fluidpredictive model using node sensor responses as input to the reversetransformation.
 16. The method of claim 15, wherein determining thevalue for a node sensor response and determining the value for a mastersensor response comprises varying temperature and pressure conditionsfor a plurality of node sensor responses and master sensor responses.17. The method of claim 15, wherein adjusting the master sensor channelselection to simulate a channel response of the node sensor comprises:identifying a set of cross-sensor linearized coefficients for a nodesensor channel based on a plurality of training fluids; and obtainingthe channel response of the node sensor on a plurality of applicationfluids with the set of cross-sensor linearized model coefficients. 18.The method of claim 15, wherein obtaining a reverse transformation usingthe simulated channel responses of the node sensor comprises combiningthe node sensor response on a plurality of training fluids and aplurality of application fluids to develop the reverse transformationmodel with a neural network.
 19. The method of claim 15, furthercomprising adjusting a master sensor channel selection from a mastersensor to simulate a node sensor channel response from a node sensor.20. The method of claim 19, wherein the master sensor channel has thesame or different nominal element as the node sensor channel.
 21. Amethod, comprising: introducing a tool into a wellbore drilled into oneor more subterranean formations, the tool having been previouslycalibrated for operation by: obtaining a plurality of master sensorresponses with a master sensor in a set of training fluids; obtaining aplurality of node sensor responses with a plurality of node sensors inthe set of training fluids, each of the plurality of node sensors andthe master sensor including an optical element; finding a linearcorrelation between a compensated master data set and a node data setfor the set of training fluids; generating a plurality of node sensorresponses in a tool parameter space from the compensated master data seton a set of application fluids; and obtaining a reverse transformationbased on the plurality of node sensor responses in a complete set ofcalibration fluids, wherein the complete set of calibration fluidscomprises the set of training fluids and the set of application fluids;determining a fluid characteristic from the plurality of node sensorresponses in the synthetic parameter space using the reversetransformation and a synthetic fluid predictive model; and modifyingoperation parameters of a drilling or a well testing and samplingaccording to the fluid characteristic.
 22. The method of claim 21,wherein obtaining a plurality of node sensor responses with a pluralityof node sensors in the set of training fluids during the toolcalibration comprises determining a temperature setting and a pressuresetting of the reduced set of training fluids according to a temperaturesetting and a pressure setting of the master set of training fluids. 23.The method of claim 21, further comprising, during the tool calibration,selecting one of the plurality of master sensors and one of theplurality of node sensors from two sensors having at least one ofdifferent designs, different configurations, or different fabricationbatches.